University of Massachusetts Amherst
	Department of Mathematics and Statistics
	Statistics and Probability Seminar

Abstract: A hidden Markov model (HMM) consists of two random processes: a state sequence X_1, X_2, . . . and an observation sequence Y_1, Y_2 , . . . The state sequence is unknown (hidden), while the observation sequence is seen. The state sequence is a Markov chain and, at each time t, the observation Y_t depends on the state of the system- that is, the value of X_t . Hidden Markov models saw early use in speech recognition, but have seen applications in many other settings, including modeling ion channels, genetic sequences, and seismological activity. We will review HMM’s, including parameter estimation algorithms, and then give a straightforward extension that allows us to forecast future observations, given past observations. That is, we will give the (calculable) density of Y_t+k, conditional on the values of Y_1 , . . . , Y_t for any k ≥ 1. We will give two examples: (1) the “occasionally dishonest casino” of Durbin et al. (Biological Sequence Analysis), and (2) forecasting mainshock earthquake activity in southern California (joint work with John Ebel, Alan Kafka, and Jenny Baglivo).